Transported Memory Networks accelerating Computational Fluid Dynamics

TL;DR

This paper addresses the challenge of accelerating industrial CFD solvers on unstructured meshes by replacing large-stencil CNN corrections with Transported Memory Networks (TMN), a memory-augmented architecture that relies on direct neighbor information and a per-cell hidden state transported with the flow. TMN couples a base FV solver with a lightweight neural corrector and a hidden-state updater, enabling autoregressive rollouts that preserve physics-inspired history while staying compatible with generic discretizations. Across 2D Kolmogorov turbulence experiments, TMN achieves comparable pointwise and spectral accuracy to CNN-based approaches but with significantly better computational efficiency, with 2–8 hidden states sufficing depending on the metric. The work suggests strong potential for integrating TMN into industrial FV codes and outlines future extensions to 3D unstructured meshes, boundary handling, and adaptive time stepping.

Abstract

In recent years, augmentation of differentiable PDE solvers with neural networks has shown promising results, particularly in fluid simulations. However, most approaches rely on convolutional neural networks and custom solvers operating on Cartesian grids with efficient access to cell data. This particular choice poses challenges for industrial-grade solvers that operate on unstructured meshes, where access is restricted to neighboring cells only. In this work, we address this limitation using a novel architecture, named Transported Memory Networks. The architecture draws inspiration from both traditional turbulence models and recurrent neural networks, and it is fully compatible with generic discretizations. Our results show that it is point-wise and statistically comparable to, or improves upon, previous methods in terms of both accuracy and computational efficiency.

Figures (10)

• Figure 1: Hybrid solver-in-the-loop approach which additionally to physics variables introduces long term memory states. These memory states are transported along the fluid flow as the physics variables are. The corresponding evolution is handled by the Transported Memory Cell (see Figure \ref{['fig:cell']}), which combines a classical base physics solver with a ML-based augmentation allowing to coarse grain discretiziation without loss of prediction accuracy.
• Figure 2: Schematic sketch of the architecture of the transported memory cell, combining a classical base physics solver with a ML-based augmentation. For the specific neural network architectures see Figure \ref{['fig:stencil_arch']} and \ref{['fig:nets_architecture']}.
• Figure 3: Input stencil for the corrector for a given cell on the forced turbulence : $64\times64$ grid on $[0;2\pi]\times[0;2\pi]$ domain. Case taken from kochkov2021machine.
• Figure 4: Simulation time until correlation drops below 0.95 for models with different input stencil sizes and 4 random initializations, vertical lines indicate the multiples of cells required by base solver to achieve the respective timings.
• Figure 5: Simulation time until correlation drops below 0.95 for models with number of hidden states (hs) and 4 random initializations. For more details on the simulation settings, c.f., Section \ref{['subsec:setting']}.